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In IRT, item difficulty is expressed in terms of trait level. Specifically, an
item’s difficulty is defined as the trait level required for participants to have a
0.50 probability of answering the item correctly. If an item has a difficulty of 0,
then an individual with an average trait level (i.e., an individual with a trait level
of 0) will have a 50/50 chance of correctly answering the item. For an item with
a difficulty of 0, an individual with a high trait level (i.e., a trait level greater than
0) will have a higher chance of answering the item correctly, and an individual
with a low trait level (i.e., a trait level less than 0) will have a lower chance of
answering the item correctly.
Item Discrimination
Just as the items on a test might differ in terms of their difficulties (some items are
more difficult than others), the items on a test might also differ in terms of the
degree by which they can differentiate individuals who have high trait levels from
individuals who have low trait levels. This item characteristic is called item dis-
crimination, and it is analogous to an item–total correlation from classical test the-
ory (CTT) perspectives [ 56 ].
An item’s discrimination value indicates the relevance of the item to the trait
being measured by the test. An item with a positive discrimination value is at least
somewhat consistent with the underlying trait being measured, and a relatively
large discrimination value (e.g., 3.5 vs. 0.5) indicates a relatively strong consis-
tency between the item and the underlying trait. In contrast, an item with a dis-
crimination value of 0 is unrelated to the underlying trait supposedly being
measured, and an item with a negative discrimination value is inversely related to
the underlying trait (i.e., high trait scores make it less likely that the item will be
answered correctly). Thus, it is generally desirable for items to have a large posi-
tive discrimination value.
IRT Measurement Models
From an IRT perspective, we can specify the components affecting the probability
that an individual will respond in a particular way to a particular item. A measure-
ment model expresses the mathematical links between an outcome (e.g., a respon-
dent’s score on a particular item) and the components that affect the outcome (e.g.,
qualities of the respondent and/or qualities of the item).
A variety of models have been developed from the IRT perspective (Table 2.1),
and these models differ from each other in at least two important ways. One is in
terms of the item characteristics, or parameters, that are included in the models. A
second is in terms of the response option format.
The simplest IRT model is often called the Rasch model or the one-parameter
logistic model (1PL). According to the Rasch model, an individual’s response to a
M. El Gaafary